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### Circle Tangent to Line

```
Date: 04/19/2001 at 17:25:36
From: Lewis
Subject: Given 2 points and tangent, determine circle

I've had trouble finding the circle that passes through two given
points and is tangent to a line. Knowing where the circle touches the
tangent has stumped me. I've drawn the perpendicular bisector between
the points and the perpendicular from the tangent, but stop there.
```

```
Date: 04/19/2001 at 18:25:41
From: Doctor Jaffee
Subject: Re: Given 2 points and tangent, determine circle

Hi Lewis,

You're almost there. The perpendicular bisector that you constructed
between the two given points must pass through the center of the
circle. Furthermore, the length of the segment that connects the
tangent line and the perpendicular bisector must equal the length of
the radius.

So, set the radius of your compass equal to the length of the segment
that connects the tangent line and the perpendicular bisector, and
place the point of your compass on one of the given points. Where the
arc crosses the perpendicular bisector will be the center of your
circle.

If you need an algebraic solution, you can use an analogous procedure.

I hope this works for you. Let me know if you have any difficulties.

- Doctor Jaffee, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry

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